Preston—On the Continuity of Isothermal Transformation, &c. 123 
Now, equation (2) gives on 
V2 
r= 
mo —pP Vz—V, 
(7) 
Therefore, (6) becomes 
(0—a)(m—p) = 5-7 P(=2-). (8) 
Vo ae Vv) 
Consequently, since the right hand member of this equation remains constant, 
the equation of the isothermal curve assumes the hyperbolic form 
(v—2,)(a—p)* = constant. (9) 
This equation holds for a spherical bubble of vapour surrounded by its own 
liquid, and in this case it is to be noted, that p must always be less than a, or 
the external pressure of the mass must be less than the normal saturated vapour 
pressure, and this is what is indicated by the portion MC of the isothermal, 
lying below the right line B D in fig. 2. 
So far, we have considered the case of a single bubble, surrounded by its 
own liquid, but the foregoing reasoning will apply when a number of equal 
bubbles are formed. If the bubbles are of different sizes, however, the capillary 
pressures, arising from the curvatures of their surface films, will be different, and 
equilibrium will be impossible—the larger bubbles tending to expand, and the 
smaller to collapse. 
It would appear, therefore, that the mass might be gradually transformed 
from the liquid to the gaseous condition, by allowing a system of equal bubbles 
to gradually imecrease in size while the volume 
increased to v, and the external pressure to a, 
and this value would be reached if the bubbles 
could be supposed to increase gradually till the 
whole mass reached the state of vapour. Long 
before this final condition can be reached, however, 
the liquid portions of the mass, which interlace the 
bubbles and fill the spaces between them, would be 
drawn out into thin films, and the conditions would 
be such, that the foregoing reasoning could not be 
applied. The action of the distended surface film, 
in fact, will be such as to draw the liquid parts, 
which fill the spaces between the bubbles, into 
spherical drops, so that a stage is ultimately reached in which the mass consists 
of a system of spherical drops, surrounded by their own vapour (fig. 4). 
The state of affairs is now reversed, for instead of having vapour in contact 
with a concave liquid surface, and therefore at a pressure less than m, the 
020 
fo) 
oO 
